相关论文: On higher-order Fourier analysis in characteristic…

The purpose of this paper is to introduce and investigate some basic properties of mixed homogeneous Herz-Hardy spaces $H\dot{K}_{\vec{p}}^{\alpha, q}(\mathbb{R}^n)$ and mixed non-homogeneous Herz-Hardy spaces $HK_{\vec{p}}^{\alpha,…

We describe graded commutative Gorenstein algebras ${\mathcal E}_n(p)$ over a field of characteristic $p$, and we conjecture that $\mathrm{Ext}^\bullet_{\mathsf{Ver}_{p^{n+1}}}(1,1)\cong{\mathcal E}_{n}(p)$, where $\mathsf{Ver}_{p^{n+1}}$…

We observe that the definition of Shelah's classical $\mathrm{NSOP}_{n}$ hierarchy for first-order theories, for integers $n \geq 3$, can be restated so that it extends to the case where $n$ is replaced with any real number $r \geq 3$.…

Classical variational Hodge structure theory characterizes the algebraicity of Hodge classes by studying the transversality of period mappings under geometric deformations. However, when algebraic varieties lack appropriate deformation…

This paper extends the foundational reflection theory of Nichols algebras to the setting of some certain coquasi-Hopf algebras. Our primary motivation arises from the classification of pointed finite-dimensional coquasi-Hopf algebras. We…

Let $H$ be a Hilbert space and $H_1,...,H_n$ be closed subspaces of $H$. Denote by $P_k$ the orthogonal projection onto $H_k$, $k=1,2,...,n$. Following Patrick L. Combettes and Noli N. Reyes, we will say that the system of subspaces…

We examine the first non-vanishing higher homotopy group, $\pi_p$, of the complement of a hypersolvable, non--supersolvable, complex hyperplane arrangement, as a module over the group ring of the fundamental group, $\Z\pi_1$. We give a…

We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…

We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet another proof for it. This new proof combines several ingredients and advantages of existing proofs, which make it very well-suited for…

Root-finding method is an iterative process that constructs a sequence converging to a solution of an equation. Householder's method is a higher-order method that requires higher order derivatives of the reciprocal of a function and has…

We prove several characterizations of the Hardy spaces for Fourier integral operators $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, for $1<p<\infty$. First we characterize $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ in terms of…

We study the {pair correlations between} prime numbers in an interval $M \leq p \leq M + L$ with $M \rightarrow \infty$, $L/M \rightarrow \beta > 0$. By analyzing the \emph{structure factor}, we prove, conditionally on the {Hardy-Littlewood…

We construct families of cell complexes that generalize expander graphs. These families are called non-$k$-hyperfinite, generalizing the idea of a non-hyperfinite (NH) family of graphs. Roughly speaking, such a complex has the property that…

We study connected mod p finite A_p-spaces admitting AC_n-space structures with n<p for an odd prime p. Our result shows that if n is greator than (p-1)/2, then the mod p Steenrod algebra acts on the mod p cohomology of such a space in a…

P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for quantum logic what Boolean algebras are for classical logic. P-algebras have type <X, 0, ', .> where 0 is a constant, ' is unary and . is…

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…

In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples,…

In this paper it is shown that for locally trivial complex analytic morphisms between some reduced spaces the Relative Riemann-Hilbert Theorem still holds up to torsion, i.e. tame flat relative connections on torsion-free sheaves are in…

Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…

Let $\mathfrak{g}$ be a Lie algebra in characteristic zero equipped with a vector space decomposition $\mathfrak{g}=\mathfrak{g}^-\oplus \mathfrak{g}^+$, and let $s$ and $t$ be commuting formal variables. We prove that the…